JBMO-SL 2007 G4

Let $S$ be a point inside $\angle pOq$ , and let $k$ be a circle which contains $S$ and touches the legs $Op$ and $Oq$ in points $P$ and $Q$ respectively. Straight line $s$ parallel to $Op$ from $S$ intersects $Oq$ in a point $R$ . Let $T$ be the intersection point of the ray $PS$ and circumscribed circle of $\vartriangle SQR$ and $T \ne S$ . Prove that $OT // SQ$ and $OT$ is a tangent of the circumscribed circle of $\vartriangle SQR$ .